Gaussian curvature | Wolfram Resource System

AntonAntonov/DimensionReducers

Dimension reduction algorithms

GaussianCurvature

Compute the Gaussian curvature of a surface

BrioschiCurvature

Compute the Gaussian curvature for a metric

NormalCurvature

Compute the normal curvature of a curve on a surface

PrincipalCurvatures

Compute the principal curvatures of a surface

Curvature

Compute the curvature of a curve

GaussianBeam

Represent a Gaussian beam and its parameters

ImplicitCurvature

Compute the implicit curvature of a curve

CurvaturePlot

Plot a curve defined by its curvature

MeanCurvature

Compute the mean curvature of a surface

RicciCurvature

Compute the components of the Ricci curvature for a metric

HermiteGaussianBeam

Represent a Hermite–Gaussian beam and its properties

GaussianQuadratureMatrix

Symmetric tridiagonal matrix for Gaussian quadrature

TotalSignedCurvature

Compute the total signed curvature of a curve

LaguerreGaussianBeam

Represent a Laguerre–Gaussian beam and its properties

GaussianQuadratureWeights

Get a numerically sorted list of abscissa-weight pairs for Gaussian quadrature

GaussianIntegerQ

Determine if a number is a Gaussian integer

GaussianQuadratureError

Find the error in the Gaussian quadrature approximation of a function’s integral

GaussianHessenbergDecomposition

Compute the Gaussian Hessenberg decomposition of a matrix

ExtrinsicCurvatureTensor

Represent the extrinsic curvature tensor field for a Riemannian submanifold

ModifiedGaussianQuadratureWeights

Get a numerically sorted list of abscissa-weight pairs for various modifications of Gaussian quadrature

CurvatureTorsionPlot3D

Plot a curve defined by its curvature and torsion

GeneralizedGaussianQuadratureWeights

Get a numerically sorted list of abscissa-weight pairs for generalized Gaussian quadrature

FocalSet

Compute the focal set of a surface

WolframRicciCurvatureScalar

Compute the Wolfram–Ricci scalar curvature of a graph and its associated properties

WolframRicciCurvatureTensor

Compute projections of the Wolfram–Ricci curvature tensor of a graph and many associated properties

NDSolveAround

Propagate Gaussian uncertainty through NDSolve

Sample Video: Surfing (Noisy)

Video of a person surfing with added gaussian noise

Sample Video: Skating (Noisy)

Video of a person skating with added gaussian noise

OsculatingCircle

Get the osculating circle of a curve

RandomUnimodularMatrix

Return a pseudorandom unimodular matrix

ColumnSpaceBasis

Return a basis for the subspace spanned by the columns of a matrix

RayTransferMatrix

Calculate the ray transfer matrix of a Gaussian optical system

OsculatingCircleProperties

Compute the defining properties of the osculating circle for a curve at a point

TangentialAngle

Compute the tangential angle of a curve

IndependentComponentAnalysis

Decompose a matrix into Independent Component Analysis matrix factors

Efficient Image Zooming Using Multiscale Pyramids

Create a Gaussian image pyramid for zooming into a large image

QuadratureWeightsToJacobiMatrix

Recover a Jacobi matrix from a list of abscissa-weight pairs

Smooth the Boundary of a Region

Use the curvature flow image filter to smooth the boundary of a snowflake

CesaroEquation

Compute the Cesàro equation for a planar curve

PivotColumns

Get the positions of the columns that are pivot columns of a matrix

EinsteinTensor

Represent the Einstein curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold

BitStringRowReduce

A memory efficient form of Gaussian elimination to row echelon form modulo 2

RicciTensor

Represent the Ricci curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold

StieltjesJacobiE

Evaluate the Stieltjes-Jacobi polynomial

RiemannTensor

Represent the Riemann curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold

Multiscale Image Representation with Image Pyramids

Create Gaussian and Laplacian pyramids to facilitate efficient multiscale image processing

BinormalVector

Compute the binormal vector of a curve

CurveTorsion

Compute the torsion of a curve

RowSpaceBasis

Return a basis for the subspace spanned by the rows of the matrix

AsymptoticCurves

Compute the asymptotic curves of a parameterized surface

EvolutoidCurve

Compute the evolutoid of a curve

EvoluteCurve

Compute the evolute of a curve

CrystalBallDistribution

Define a continuous probability distribution characterized by a Gaussian core and a power-law tail

GeneralizedHelicoid

Compute the generalized helicoid of a curve

Intrinsic3DCurve

Plot intrinsic curves in 3D

SalzerPiessensInversionWeights

Get a list of abscissas and weights for the numerical inverse Laplace transform

RicciScalar

Compute the Ricci scalar for a metric

NaturalEquations

Compute the natural equations of a curve

MultinormalKLDivergence

Compute the Kullback–Leibler divergence between two multinormal distributions

HeegnerPrime

Convert integer tuples into Heegner field primes when applicable

ExtrinsicCurvedManifoldToGraph

Produce random spatial graphs by sprinkling points into a Riemannian manifold with an arbitrary extrinsic curvature

CurvedSpacetimeSprinkling

Produce random causal graphs by sprinkling points into a spacetime with a specified algebraic curvature function

BitStringLinearSolve

A memory efficient form of solving linear systems modulo 2

PivotedLUDecomposition

Compute the LU decomposition of a matrix with different pivoting methods

Magnetic Potential inside an Electric Motor

Find a fit for measured BH-curve data with a Gaussian model to solve a magnetostatic problem

UpperTriangularDecomposition

Find an upper triangular form and conversion matrix for a given matrix

BitStringNullSpace

A memory efficient form of computing the null space of a matrix modulo 2

IntrinsicCurvedManifoldToGraph

Produce random spatial graphs by sprinkling points into a Riemannian manifold with a specified intrinsic algebraic curvature function

Multiscale Feature Detection

Apply gradient filtering or saliency filtering to images

Smooth Image Assembly using Multiscale Blending

Split and merge two images at different scales using image pyramids

ADMDecomposition

Represent a canonical decomposition of the metric for a Riemannian or pseudo-Riemannian manifold via the ADM formalism

SolveVacuumEinsteinEquations

Determine whether a given Riemannian or pseudo-Riemannian manifold is a solution to the vacuum Einstein field equations

StressEnergyTensor

Represent a stress-energy tensor (field) over a Riemannian or pseudo-Riemannian manifold

SolveEinsteinEquations

Determine whether a given stress-energy tensor (field) is a solution to the Einstein field equations

ChristoffelSymbols

Represent the Christoffel symbols for (the Levi-Civita connection over) a Riemannian or pseudo-Riemannian manifold

SolveVacuumADMEquations

Determine whether a given ADM decomposition is a solution to the vacuum ADM equations

OsculatingParabola

Get the osculating parabola of a plane curve

OsculatingConic

Get the osculating conic of a plane curve

RadiusOfAberrancy

Compute the radius of aberrancy of a plane curve

Geodesic

Compute the geodesics for a parametrized surface

CurveAberrancy

Compute the aberrancy of a plane curve

AberrancyCurve

Compute the curve of aberrancy of a plane curve

NormalTexture

Generate a normal texture from height data

ApartAll

Compute a partial fraction decomposition over the algebraic closure of the rationals

TsallisEntropy

Compute the Tsallis entropy

EisensteinFactorInteger

Factor an integer into powers of Eisenstein primes

RandomMatrix

Get a pseudorandom matrix of a given kind, type and size

Interactively View Fluorescent Uptake of Cells

Segment and identify cells with more than a certain fluorescent uptake

Image Vectorization

Apply smoothing and quantization to a raster image to make it more suitable for vectorization

EisensteinIntegers

Support arithmetic operations for pairs of Eisenstein integers

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